TY  - BOOK
AU  - Grabovsky Yury
TI  - Composite materials : : mathematical theory and exact relations 
SN  - 9780750310499
AV  - TA418.9.C6 GRA 
PY  - 2016///
PB  - IOP Publishing
KW  - Composite materials
KW  - Materials science
KW  - Mathematics
KW  - Physics
KW  - Mathematical & Computational
KW  - Mathematical physics
KW  - Composites
N1  - Includes a bibliography; 
Preface
1. Introduction
part I. Mathematical theory of composite materials. 2. Material properties and governing equations
2.1. Introduction
2.2. Conductivity and elasticity
2.3. Abstract Hilbert space framework
2.4. Boundary value problems
2.5. Geometry of local spaces. 3. Composite materials
3.1. Mathematical definition of a composite
3.2. Periodic composites
3.3. Properties of H-convergence. part II. General theory of exact relations and links
4. Exact relations
4.1. Introduction
4.2. L-relations
4.3. Sufficient conditions for stability under homogenization
4.4. Special types of exact relations
4.5. Proofs of theorems 4.8, 4.12, 4.11. 5. Links
5.1. Links as exact relations
5.2. Algebraic structure of links
5.3. Volume fraction formulas as links. 6. Computing exact relations and links
6.1. Finding Jordan A-multialgebras
6.2. Computing exact relations
6.3. Computing volume fraction relations
6.4. Finding Jordan A^-multialgebras
6.5. Computing links. part III. Case studies
7. Introduction. 8. Conductivity with the Hall effect
8.1. Two-dimensional conductivity with the Hall effect
8.2. Three-dimensional conductivity with the Hall effect
8.3. Fibrous conducting composites with the Hall effect. 9. Elasticity
9.1. Two-dimensional elasticity
9.2. Three-dimensional elasticity
9.3. Fibrous elastic composites. 10. Piezoelectricity
10.1. Exact relations
10.2. Links
10.3. Two-dimension-specific relations and links. 11. Thermoelasticity
11.1. Two-dimensional thermoelasticity
11.2. Three-dimensional thermoelasticity
12. Three-dimensional thermoelectricity. part IV. Appendices
A. E- and J -regularity for conductivity and elasticity
B.A polycrystalline L-relation that is not exact
C. Multiplication of SO(3) irreps in endomorphism algebras
N2  - The mathematical method of composites has reached a very high level of maturity and developments have increased our understanding of the relationship between the microstructure of composites and their macroscopic behaviour. This book provides a self-contained unified approach to the mathematical foundation of the theory of composites, leading to the general theory of exact relations. It also provides complete lists of exact relations in many specific physically relevant contexts, such as conductivity, fibre-reinforced elasticity, piezoelectricity, thermoelectricity and more
ER  -